A^3-a^2+21a+45=0

Solution for A^3-a^2+21a+45=0 equation:

^3-A^2+21A+45=0

We add all the numbers together, and all the variables

-1A^2+21A=0

a = -1; b = 21; c = 0;
Δ = b2-4ac
Δ = 212-4·(-1)·0
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-21}{2*-1}=\frac{-42}{-2}
=+21
$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+21}{2*-1}=\frac{0}{-2}
=0
$